{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5STG7DCKM7RCCB3PNNK7CXCJ4L","short_pith_number":"pith:5STG7DCK","canonical_record":{"source":{"id":"1209.4850","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2012-09-21T15:49:14Z","cross_cats_sorted":["cs.CV","math.MP"],"title_canon_sha256":"71783c12ef72955fe5f33aea6bbcaa5b0f6c1479b2cffc31b32139dadae62806","abstract_canon_sha256":"91bc3e91bd87bbf9ce48d40b984b5c6e51ed49ef4b6c6ac0e8168304b319abe7"},"schema_version":"1.0"},"canonical_sha256":"eca66f8c4a67e221076f6b55f15c49e2c4d7b551222e932a7aee7a35795a1385","source":{"kind":"arxiv","id":"1209.4850","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4850","created_at":"2026-05-18T03:28:19Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4850v2","created_at":"2026-05-18T03:28:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4850","created_at":"2026-05-18T03:28:19Z"},{"alias_kind":"pith_short_12","alias_value":"5STG7DCKM7RC","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5STG7DCKM7RCCB3P","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5STG7DCK","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5STG7DCKM7RCCB3PNNK7CXCJ4L","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4850","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2012-09-21T15:49:14Z","cross_cats_sorted":["cs.CV","math.MP"],"title_canon_sha256":"71783c12ef72955fe5f33aea6bbcaa5b0f6c1479b2cffc31b32139dadae62806","abstract_canon_sha256":"91bc3e91bd87bbf9ce48d40b984b5c6e51ed49ef4b6c6ac0e8168304b319abe7"},"schema_version":"1.0"},"canonical_sha256":"eca66f8c4a67e221076f6b55f15c49e2c4d7b551222e932a7aee7a35795a1385","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:19.557225Z","signature_b64":"OaPaSbqoj/1WAMdCqwEVJAbUpvAsC69rooIxqSjtfxzsZCy6pe1vTCzF0JEdMej+YZ8o/ArqEm4/xx50xDpMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eca66f8c4a67e221076f6b55f15c49e2c4d7b551222e932a7aee7a35795a1385","last_reissued_at":"2026-05-18T03:28:19.556716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:19.556716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4850","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ervtTzcS2eDP3LOA1Ki8ZQIxSIK1exyjCmh5B32714pzoUzOeKc/dL3DlY1a1BKgz/ekyzbagoCAla/iANVqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:27:17.674786Z"},"content_sha256":"bffa282ee78a0ac5a78064877542feaaa9d8f2d94e09613b4d24a249d49d3152","schema_version":"1.0","event_id":"sha256:bffa282ee78a0ac5a78064877542feaaa9d8f2d94e09613b4d24a249d49d3152"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5STG7DCKM7RCCB3PNNK7CXCJ4L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["cs.CV","math.MP"],"primary_cat":"math-ph","authors_text":"Mireille Boutin, Shanshan Huang","submitted_at":"2012-09-21T15:49:14Z","abstract_excerpt":"We define the Pascal triangle of a discrete (gray scale) image as a pyramidal arrangement of complex-valued moments and we explore its geometric significance. In particular, we show that the entries of row k of this triangle correspond to the Fourier series coefficients of the moment of order k of the Radon transform of the image. Group actions on the plane can be naturally prolonged onto the entries of the Pascal triangle. We study the prolongation of some common group actions, such as rotations and reflections, and we propose simple tests for detecting equivalences and self-equivalences unde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4850","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wvqDbMvPc6vyrCz63V6Rd9XERwxcF+DCV+5GGmrdIB4aI5NSYp6XBq7cfVWB+hhFepIYtoRFR3UrPXvUlEE5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:27:17.675133Z"},"content_sha256":"7e136c82ff0d7eadf7d85fbab9b827deac47f3bc8f77734e5cdff4c6ed765149","schema_version":"1.0","event_id":"sha256:7e136c82ff0d7eadf7d85fbab9b827deac47f3bc8f77734e5cdff4c6ed765149"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5STG7DCKM7RCCB3PNNK7CXCJ4L/bundle.json","state_url":"https://pith.science/pith/5STG7DCKM7RCCB3PNNK7CXCJ4L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5STG7DCKM7RCCB3PNNK7CXCJ4L/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T08:27:17Z","links":{"resolver":"https://pith.science/pith/5STG7DCKM7RCCB3PNNK7CXCJ4L","bundle":"https://pith.science/pith/5STG7DCKM7RCCB3PNNK7CXCJ4L/bundle.json","state":"https://pith.science/pith/5STG7DCKM7RCCB3PNNK7CXCJ4L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5STG7DCKM7RCCB3PNNK7CXCJ4L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5STG7DCKM7RCCB3PNNK7CXCJ4L","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"91bc3e91bd87bbf9ce48d40b984b5c6e51ed49ef4b6c6ac0e8168304b319abe7","cross_cats_sorted":["cs.CV","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2012-09-21T15:49:14Z","title_canon_sha256":"71783c12ef72955fe5f33aea6bbcaa5b0f6c1479b2cffc31b32139dadae62806"},"schema_version":"1.0","source":{"id":"1209.4850","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4850","created_at":"2026-05-18T03:28:19Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4850v2","created_at":"2026-05-18T03:28:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4850","created_at":"2026-05-18T03:28:19Z"},{"alias_kind":"pith_short_12","alias_value":"5STG7DCKM7RC","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5STG7DCKM7RCCB3P","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5STG7DCK","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:7e136c82ff0d7eadf7d85fbab9b827deac47f3bc8f77734e5cdff4c6ed765149","target":"graph","created_at":"2026-05-18T03:28:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We define the Pascal triangle of a discrete (gray scale) image as a pyramidal arrangement of complex-valued moments and we explore its geometric significance. In particular, we show that the entries of row k of this triangle correspond to the Fourier series coefficients of the moment of order k of the Radon transform of the image. Group actions on the plane can be naturally prolonged onto the entries of the Pascal triangle. We study the prolongation of some common group actions, such as rotations and reflections, and we propose simple tests for detecting equivalences and self-equivalences unde","authors_text":"Mireille Boutin, Shanshan Huang","cross_cats":["cs.CV","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2012-09-21T15:49:14Z","title":"The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4850","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bffa282ee78a0ac5a78064877542feaaa9d8f2d94e09613b4d24a249d49d3152","target":"record","created_at":"2026-05-18T03:28:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"91bc3e91bd87bbf9ce48d40b984b5c6e51ed49ef4b6c6ac0e8168304b319abe7","cross_cats_sorted":["cs.CV","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2012-09-21T15:49:14Z","title_canon_sha256":"71783c12ef72955fe5f33aea6bbcaa5b0f6c1479b2cffc31b32139dadae62806"},"schema_version":"1.0","source":{"id":"1209.4850","kind":"arxiv","version":2}},"canonical_sha256":"eca66f8c4a67e221076f6b55f15c49e2c4d7b551222e932a7aee7a35795a1385","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eca66f8c4a67e221076f6b55f15c49e2c4d7b551222e932a7aee7a35795a1385","first_computed_at":"2026-05-18T03:28:19.556716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:19.556716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OaPaSbqoj/1WAMdCqwEVJAbUpvAsC69rooIxqSjtfxzsZCy6pe1vTCzF0JEdMej+YZ8o/ArqEm4/xx50xDpMBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:19.557225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4850","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bffa282ee78a0ac5a78064877542feaaa9d8f2d94e09613b4d24a249d49d3152","sha256:7e136c82ff0d7eadf7d85fbab9b827deac47f3bc8f77734e5cdff4c6ed765149"],"state_sha256":"f8146b14bceb07421c4666351a31bf0ac37933fc53f3700cf0b27e4dbbee928d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/d07/cHIe2Ck+OPJPjE9hxdcsFjAQU8vA4MDo2ajv1l896OoAPxKFOcxdE/csSfq0104qB9A6096eXPQBiHCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:27:17.677117Z","bundle_sha256":"fc984c6c8806e97fee13fe52dcaf83b54e9ca5f8a6367c132ab517e0bc7ad801"}}