From 53e0068b7024dd692baa76676ecf61f6dd46073c Mon Sep 17 00:00:00 2001
From: Michael Zaikin <michael.zaikin@starkware.co>
Date: Mon, 21 Oct 2024 13:15:56 +0100
Subject: [PATCH] Update images

---
 docs/img/utreexo_delete.svg    |  6 +++---
 docs/img/utreexo_pollard.svg   | 14 +++++++-------
 docs/img/utreexo_positions.svg |  6 +++---
 docs/img/utreexo_proof.svg     |  2 +-
 docs/img/utreexo_stump.svg     |  6 +++---
 docs/utreexo.md                |  5 ++++-
 6 files changed, 21 insertions(+), 18 deletions(-)

diff --git a/docs/img/utreexo_delete.svg b/docs/img/utreexo_delete.svg
index 849b3197..f8d6fdc4 100644
--- a/docs/img/utreexo_delete.svg
+++ b/docs/img/utreexo_delete.svg
@@ -1,4 +1,4 @@
-<svg version="1.1" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1683.986991975923 438.13208323699655" width="3367.973983951846" height="876.2641664739931">
+<svg version="1.1" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 2187.3968981193234 537.8064356153063" width="4374.793796238647" height="1075.6128712306127">
   <!-- svg-source:excalidraw -->
   
   <defs>
@@ -21,9 +21,9 @@
           }
 @font-face {
         font-family: Nunito;
-        src: url(data:font/woff2;base64,d09GMgABAAAAAA0QAA8AAAAAGQgAAAy0AAEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGjAbg0IcgXQGYD9TVEFURABsEQgKoGCaOwtcAAE2AiQDgQ4EIAWEJAcgG4QUo6KUs1KS/eWBDYaoNbC/OCAGsm2Ht1gro+WbZLXFtdZmtF9Tw+JCAv27IPCpHMjfz+Qo10GBa+RskgN+JgXIrsS6QlU40hWqQr0uKUMWgDI8busfovw7QJnEMHFEjrBJaW0QBMRKxCisi+z+RNWw9c4n4ZMKKCzCBR1isAhLIUzyGqEpFNf/APzfoS0HnskQwlr+VRic216/Cp7MoklpeKJVsqrteyMADI3+v/2+1bnv7Ky1h4glfojbOJ3QCIU4/z7Zf998k5011UQTb+RNRJckHlUah0wlJDKhFEgWcmBbuQTjWgs2RpkQQ93tX5/38/4Pi0APQA5CkhMpiaPa4MeQgpRKhkBqkAJ2eTXLCaiXPX0NgPpU3t4EqPwB3iegx2tfE+gGBMQxYhIzfvOHFoWnkNgF/Z/J2HC3HBdPywD/Y6f+e/sJ+F+57cLlUiDWP4Rhz9L968381/bee/mKhfycXwLHkz9HoBe42ZCuJegnFoSaz5qwWZQTKAqKnEjYTLIw+lKc7F7POGnX4ISYm4sgzgkkRMqEHsv1RCmjeD5c523/uCrNucWxLXf10twIpP+woT3gPdXWlIPfks3xgTBUcoZAGqIk06rQDXXHthpSQVyX50mdkm4Y+SJanmBSPe27bhZkheygo5AMHan8JbjprViDeLs3wGsUTsEvu9IiL5tZfREA855zAEdqNjoRUSx22wr+YvTNgQMgWkfn8/98wC1J3AMwH6z0nxyUPVmaQzoHGs5soMfrrbcdA+CvV4TBsFkNUoGp3hiaStTT1xcwYGUDRULGTHPqQMPjh7HAzMajUQufjiYYZ2JTpUEzn/bGPLbZArPNMtOMMHZKxJTVQ46c4cK1J4FgBQjfAK4AXCNKs+eyx8i3DT5z3KdlVjO13fE5CIMJlO5RQWJhmJIcpM4fKeEEERFUGxWQwIdCEGJgIWQWQ6DQG8eyiPQwIlE2Lr+DMebT8rERShmnRiOVAmsXJoMQ4CpFKG2eXixGI4w9CKZGBAysQ0oW4IoI4R8ihOAJ4q7nMgtdjFNXeE1pOUdQAjzWonB0FSxGpH0LTOgC5BjNt6INtlTfq4BQSMQEchD5mggdk2EqCOo7kN3BusCgJGAEnfz3AroFGJwjF4DgGG7IwvsNsGLYDCqemm5hw+zpwfdKPKXwub3IVdjm9IyLosAIA/Hs5N4QkDakwcy6GKYKxtp2GlhMaIQPFhLAcnqnJccyfE/n9Cp3ZkXMuRLSiOJ3GX0YG7tkDqhKehkumsGYMpiMy+l8699vzaztkg3INyprs51wYwCCDwY4ZQDBebdUi8XZ7unljrIiGZjb4Lts7zUQArvLVqJxYgo7bPGgaZq5uFxm7uwuZ29t5S+e4W5xM5RyP/EYH055mpIYKcqvic8H+1Wlw2ZVwrOwbRpzSt17myD1lALZkFYWFUQ//PrkhrRZg3VqNFLo6VjraLBqhN4THHDOY93j6RpVivHrQTaW0/oZDO+UgquwHKhMru9RhaE1G/Dmh51t1g2v19AYExYMjCEuxM5b0Ecm4RwQi+5Pd1vLzQnj6Ho77zCn0si0ngEa1oZwMNhsQ0Tq6jabRQZiC1q9SL12aQOYFI9rAUoBqUuHNKdlLlAbysIcel3QYLZ+AQc6TMNjWHuIsqJ3iTxMmVN+2ZGtPSvYasCYEiBHhQgJibAiC7/6LsPXrUezupggSVpLQOqyEYI+e31H1Gd0UrwA7O2kLHYheBILp+wKBcszHHj+q9Rth8yMkw5gOwtAOBJw1ukkcZPWAHaNPmMxEQB7AybnEp+s32Z0q53qti1qdkiGuEr6xGRrmpj9fs32Iht+iXJCZJY6fWKv/LzEPnV6i8wZqvq1kOHteXNQCwsMD5kZUnx8tAfX7tqy2iUbXJg3ROqeap1grmQaTUxP8shhw4dNAINwcA96LX04/M7Xq7naM7o134G3dC9cs8VqTTGbrWbrFuAX68s0CT6LNb5FPT6DoVj/ldBL98BwJ91H74JpXfTChc9LDGiqWC9kZavzLIVGVC9gT38t1iIglN2iSWqxZGla63TJMVakb0SeAkLIuSpdYDwjbak42iRm2xJwBa5CO2IkPXkx4F/89Bu4ghAwCQd30XtqyLFQcAzZNZxbXlJV+N/DhxEO8/0Fti1FGsG5NkpMMBRL8fSUgYdxpiXP+Y3eSYM76e/jFwm6XyhbMJdG8WcNgEAXjtZFn2H+nmgeumshz6lWazNVp4PgIp1WniJiO404ehcN7qL76XfHK43W5Ff0Gvj5JmSALq02SdlqUSFFSYZcViJAi1Y8c0Kpm3XsonXBlmQu7aEXLvxWbDAaSjUJLVZLvK8GmaHRX7hr2U+Ul8RmYmAxC3VJO9l7t+B/u5OM2A/RWL9EA2TApaTqXtFrAJnaKuRlq77payeob7RNheFoY88auYGe7+TXEyjT8APOUoKGHd7cCb6ta1Guy4DrtN44bViiJiPb+Pb5Uc6QieEauvuAMk8DUL367VrfpZjfZLf37rttY4diYaPDbrVZRk6alDXMrtgwsfkQwWyKi0xxUPpxoycW3xgEuUc8H5n/YlUgyU51tFNNFIqZCgaFeKjE7btvvaKi+VJVisYsygrLvNkKPD1PjK9nK9MqxHHOJFG4LdGx5vyt8DTG28aiaotaf3NmStSkF6udIdIYU4RAoLFoMlNoTjLFQdOK7/EFickKI5oZ0nBiAim3583xdSxlcgUaZ1OiUSkLZhLSiLaS1CRVQb0MLOhDv816GF5MI+58KtiwbjxEHhay3Qw7KFQHbK6nd5le+EIDR4UCBUULcvHECDc08EZvV5hMZmJno0aLwyQ0R1ysyQykxJPdVBfVTnVQKE4qQghbXoDKTWWKhCqTUeWpVwJzN2eHPWlmYxFvdEZpXYxZWorYlntzSa03wpLpbJ1bK+ldnI+vic92ofHaEmVipdGo9FarUrPQrxyTWMwxfUVvnzdYgYOaMwZqyrhlVCeZ4qSOpg6hQJ39JBn9xwGUrUWicetiBFmpsqeQITCrxKBWOWvRtPRaVOlUo6z09yug5O7usnSdxt0iyc7Iceh0ekdSjt2ZpNc5dbY0mSFCzlNadSkpFp1SZdGDn0bKmKXLvbmg9WaqqX2KtshNsDnRhFVVBpOypp3R1W5LmlXCnzQ7X6TnsU1iCduo54rQrxyjRMwxfQN7/dNcDY2JsG3ILE66s64hkWafNktNe5QyS2gTZIhoD1NmCuyCLNDMZJIANDYzJ+bn8q35P+3R01IJhBdNhJRYFgJBEHBDBhJx8Yi23mv7h0RFMannxDc8m9NvTDJRWKI9Xzis95yWTvxqJgIBqJ1Yvoky8WTeFs/P4jeh7H3MqJW86GAIIkHBXN5aRlgJm3oW/Tl0S9qnzPxPqEtXxwphAX5pspRXrQ8HAZYcGxw9hxwXRFjSe+mnlBwKOZ7yCQkikcikICQ6ODZxymHyxCtkcMByzZTWk6mLPSc0jHDecS6/gwvX/63+3i0/HXgIQU5BJAgC0PtCANvNWy9CxSUmBJy02a76ylRxhS1BEblBd1y+OXGbuDclUW3NjOzmxfpHqFLTlMJsPWsbZzaXt5LNOcnjnwR9sSSpvHmljXGAxYRIwat6FawlEW4eLtyuF4O9nYNtrUKUPi0598tNyFGbTDnqBO4zbzJtX6TI1aYlolikG4sOYaN6sKJHvM0MxiYebxODsRks6HQe604kbk5dFvxJa6wZkf+lTT93qFNTVUKLgY1mu+qqUtAqezzvOuckj3eSw17J564E/gvgQCSqU0A4oBXQUPE23s47eCfv4t28h/dqfY8BP3T/AbDtR/rlBKRoKsox6RUmW47gKld3jmIVLAswoA4kqwtyEJeKdOCDG6KgBBDkvDgMsN+TTw373l2tNN9irH0JwBP60qsAeB67NOH/yPKKHQQgZAAIX5G0hrBo+G+zC7XVF7FZTJ3XXOl7XJVJHPiC5YStEdI7xTITjdik0qtRXMjTngRSMxA258SNwAc6iAUxZEESKEH6rcdUH4h0XCwMElx8UZBXhYE2uyIBrvPP1NSvlLkDS90EuOfHY72MO7HeKN1fb23rnOzw9YE2RetCo6RtBLk+AeJNEPCUeotPBU5o1qhcE4tqVWp1aJSuXbkGtSq5VatVw6udVYcmtdo1S9ZDO59yWdhUiQeVq1pQm6Bmxpci4kglihZ7c1WzymaVPI6eIYdqBDXgU328mZFpRoRMlKNb9OTDvl6saDHiIZy8qiEelY1PUZ1RVlLJgFA7STZXMAch8KHatWhKRbaXNTzyUmoqSFU2MxqEouaipkE1T7NQO5lkalCkEiGs3Y78cREAAAA=);
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diff --git a/docs/img/utreexo_pollard.svg b/docs/img/utreexo_pollard.svg
index 209a862c..f1cb36b4 100644
--- a/docs/img/utreexo_pollard.svg
+++ b/docs/img/utreexo_pollard.svg
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diff --git a/docs/img/utreexo_positions.svg b/docs/img/utreexo_positions.svg
index 71fdbc6b..4c7c8e36 100644
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diff --git a/docs/img/utreexo_proof.svg b/docs/img/utreexo_proof.svg
index c1c80f4c..e399facd 100644
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\ No newline at end of file
diff --git a/docs/img/utreexo_stump.svg b/docs/img/utreexo_stump.svg
index ede9a586..eb001e76 100644
--- a/docs/img/utreexo_stump.svg
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37.73092256237669)"><path d="M0 0 C30.69 0, 61.39 0, 81.95 0 M81.95 0 C81.95 15.14, 81.95 30.29, 81.95 75.46 M81.95 75.46 C49.18 75.46, 16.41 75.46, 0 75.46 M0 75.46 C0 58.75, 0 42.03, 0 0" stroke="#1e1e1e" stroke-width="1.5" fill="none" stroke-dasharray="8 9"></path></g><g transform="translate(1173.151384474924 625.0998365752766) rotate(0 11.610000610351562 24.300000000000182)"><text x="11.610000610351562" y="36.144000000000005" font-family="Nunito, Segoe UI Emoji" font-size="36px" fill="#1e1e1e" text-anchor="middle" style="white-space: pre;" direction="ltr" dominant-baseline="alphabetic">1</text></g><g transform="translate(1268.1359067689502 626.5213608099748) rotate(0 83.3579910993576 24.300000000000182)"><text x="0" y="36.144000000000005" font-family="Nunito, Segoe UI Emoji" font-size="36px" fill="#1e1e1e" text-anchor="start" style="white-space: pre;" direction="ltr" dominant-baseline="alphabetic">leaves = 6</text></g><g stroke-linecap="round"><g transform="translate(1115.4257399858204 261.64342399242014) rotate(0 -15.869140625 -36.82047526041606)"><path d="M0 0 C-5.29 -12.27, -26.45 -61.37, -31.74 -73.64 M0 0 C-5.29 -12.27, -26.45 -61.37, -31.74 -73.64" stroke="#1e1e1e" stroke-width="1" fill="none"></path></g><g transform="translate(1115.4257399858204 261.64342399242014) rotate(0 -15.869140625 -36.82047526041606)"><path d="M-14.59 -55.45 C-18.86 -59.98, -23.14 -64.52, -31.74 -73.64 M-14.59 -55.45 C-19.94 -61.12, -25.28 -66.8, -31.74 -73.64" stroke="#1e1e1e" stroke-width="1" fill="none"></path></g><g transform="translate(1115.4257399858204 261.64342399242014) rotate(0 -15.869140625 -36.82047526041606)"><path d="M-30.29 -48.68 C-30.65 -54.9, -31.01 -61.12, -31.74 -73.64 M-30.29 -48.68 C-30.74 -56.47, -31.19 -64.25, -31.74 -73.64" stroke="#1e1e1e" stroke-width="1" fill="none"></path></g></g><mask></mask><g transform="translate(1094.1204014441535 281.7524734715862) rotate(0 167.3459576368332 48.600000000000364)"><text x="0" y="36.144000000000005" font-family="Nunito, Segoe UI Emoji" font-size="36px" fill="#1e1e1e" text-anchor="start" style="white-space: pre;" direction="ltr" dominant-baseline="alphabetic">"Placeholder" root</text><text x="0" y="84.744" font-family="Nunito, Segoe UI Emoji" font-size="36px" fill="#1e1e1e" text-anchor="start" style="white-space: pre;" direction="ltr" dominant-baseline="alphabetic">which does not exist</text></g><g stroke-linecap="round"><g transform="translate(1155.643838944154 771.156770346588) rotate(0 12.0849609375 -38.25276692708303)"><path d="M0 0 C4.03 -12.75, 20.14 -63.75, 24.17 -76.51 M0 0 C4.03 -12.75, 20.14 -63.75, 24.17 -76.51" stroke="#1e1e1e" stroke-width="1" fill="none"></path></g><g transform="translate(1155.643838944154 771.156770346588) rotate(0 12.0849609375 -38.25276692708303)"><path d="M25.25 -51.53 C24.86 -60.57, 24.47 -69.61, 24.17 -76.51 M25.25 -51.53 C24.87 -60.33, 24.49 -69.13, 24.17 -76.51" stroke="#1e1e1e" stroke-width="1" fill="none"></path></g><g transform="translate(1155.643838944154 771.156770346588) rotate(0 12.0849609375 -38.25276692708303)"><path d="M8.94 -56.68 C14.45 -63.86, 19.96 -71.03, 24.17 -76.51 M8.94 -56.68 C14.31 -63.67, 19.68 -70.65, 24.17 -76.51" stroke="#1e1e1e" stroke-width="1" fill="none"></path></g></g><mask></mask><g transform="translate(1030.822875402487 783.9904292007541) rotate(0 233.0819091796875 48.600000000000364)"><text x="0" y="36.144000000000005" font-family="Nunito, Segoe UI Emoji" font-size="36px" fill="#1e1e1e" text-anchor="start" style="white-space: pre;" direction="ltr" dominant-baseline="alphabetic">"Empty" root whose children</text><text x="0" y="84.744" font-family="Nunito, Segoe UI Emoji" font-size="36px" fill="#1e1e1e" text-anchor="start" style="white-space: pre;" direction="ltr" dominant-baseline="alphabetic">are empty nodes too</text></g></svg>
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diff --git a/docs/utreexo.md b/docs/utreexo.md
index 6a5da364..0f0d4d8f 100644
--- a/docs/utreexo.md
+++ b/docs/utreexo.md
@@ -10,6 +10,9 @@ However the accumulator scheme proposed in the paper doesn't perform well in the
 
 Check out our community call where the Utreexo accumulator is explained: https://www.youtube.com/watch?v=jq6cx6LowkA&pp=ygUYc2hpbmlnYW1pIGNvbW11bml0eSBjYWxs
 
+> [!TIP]  
+> Make sure you are familiar enough with the original Utreexo design before moving on to the next sections, as they are mostly focused on the differences between two schemes.
+
 ## Pollard
 
 The key distinction between the original and new designs is that deleted leaves are not actually removed from the forest but made "empty" instead, moreover, their remaining siblings are "promoted" to the parent node (i.e. moving upwards). The full discussion about new accumulator design: https://github.com/mit-dci/utreexo/discussions/249
@@ -55,7 +58,7 @@ Also it's worth noting that before "null" was indicating a missing roots whereas
 
 ## Batch proof
 
-Batch inclusion proofs were introduced in the Utreexo paper (see Appendix) and they can reduce the total size of proof(s) significantly. But the batch delete algorithm was pretty complex and IO intensive. The pollard scheme streamlined batch deletions and made batch proofs more practical.
+Batch inclusion proofs were introduced in the Utreexo paper (see Appendix) and they can reduce the total size of proof(s) significantly But the batch delete algorithm was pretty complex and IO intensive. The pollard scheme streamlined batch deletions and made batch proofs more practical. Pollar batch proof contains all the intermediate nodes that cannot be computed and which are required to eventually calculate the roots (going row by row, left to right, bottom top).
 
 <p align="center" width="100%">
   <img src="./img/utreexo_proof.svg" alt=""/>