{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Z2MT2PMIJ3OL43ACBUNWQQESVM","short_pith_number":"pith:Z2MT2PMI","canonical_record":{"source":{"id":"1705.10753","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-30T17:04:15Z","cross_cats_sorted":[],"title_canon_sha256":"fc779abc37eb70cd575e84680901f23a10845c7be228295ea4be937fe405e7e0","abstract_canon_sha256":"fa74b756c52eddad95f782034d2927c7f99ff6c3530fb6400c7f03df541b74a8"},"schema_version":"1.0"},"canonical_sha256":"ce993d3d884edcbe6c020d1b684092ab2287290ee3228379f46e013bccc94e39","source":{"kind":"arxiv","id":"1705.10753","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10753","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10753v2","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10753","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"Z2MT2PMIJ3OL","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z2MT2PMIJ3OL43AC","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z2MT2PMI","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Z2MT2PMIJ3OL43ACBUNWQQESVM","target":"record","payload":{"canonical_record":{"source":{"id":"1705.10753","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-30T17:04:15Z","cross_cats_sorted":[],"title_canon_sha256":"fc779abc37eb70cd575e84680901f23a10845c7be228295ea4be937fe405e7e0","abstract_canon_sha256":"fa74b756c52eddad95f782034d2927c7f99ff6c3530fb6400c7f03df541b74a8"},"schema_version":"1.0"},"canonical_sha256":"ce993d3d884edcbe6c020d1b684092ab2287290ee3228379f46e013bccc94e39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:43.659282Z","signature_b64":"fil4dYjpoe5phcl8+3ImmF0KpYdlSQsaSAYh30WCEN1S7lQZdgy8cdzSnlJLC/0MaEfLO2eMNCiWRmBKjMYRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce993d3d884edcbe6c020d1b684092ab2287290ee3228379f46e013bccc94e39","last_reissued_at":"2026-05-17T23:42:43.658632Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:43.658632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.10753","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":"2026-05-17T23:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Ik/eiDHWXqqCme1ncdzcoyNPhlKo1mu7aZNw8HCzeHaVm7pcQ3naMDXo3qi+8a3fsc3GznmynlQF+pFaHPKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:28:29.617514Z"},"content_sha256":"ad5fc8daf9d96aad65ac5eb976b574a32f4f8cc5c4f246aa259356e9ae9ddd7e","schema_version":"1.0","event_id":"sha256:ad5fc8daf9d96aad65ac5eb976b574a32f4f8cc5c4f246aa259356e9ae9ddd7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Z2MT2PMIJ3OL43ACBUNWQQESVM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tutte Polynomials of Symmetric Hyperplane Arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hery Randriamaro","submitted_at":"2017-05-30T17:04:15Z","abstract_excerpt":"Originally in 1954 the Tutte polynomial was a bivariate polynomial associated to a graph in order to enumerate the colorings of this graph and of its dual graph at the same time. However the Tutte polynomial reveals more of the internal structure of a graph, and contains even other specializations from other sciences like the Jones polynomial in Knot theory, the partition function of the Pott model in statistical physics, and the reliability polynomial in network theory. In this article, we study the Tutte polynomial associated to more general objects which are the arrangements of hyperplanes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10753","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":"2026-05-17T23:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xrDcsB0eNLpu5nvbr1NT+0XbX5XPlkh5NQq4jB69HFx6vAjqLIaNt1AF2j62a2NvtqwxS3xYEz2K3GAQmluHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:28:29.617860Z"},"content_sha256":"59da4f9a1588b6622a88987cd9d6ffad88dbe0dcada02bca5d69664a83f91894","schema_version":"1.0","event_id":"sha256:59da4f9a1588b6622a88987cd9d6ffad88dbe0dcada02bca5d69664a83f91894"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2MT2PMIJ3OL43ACBUNWQQESVM/bundle.json","state_url":"https://pith.science/pith/Z2MT2PMIJ3OL43ACBUNWQQESVM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2MT2PMIJ3OL43ACBUNWQQESVM/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":"2026-06-05T12:28:29Z","links":{"resolver":"https://pith.science/pith/Z2MT2PMIJ3OL43ACBUNWQQESVM","bundle":"https://pith.science/pith/Z2MT2PMIJ3OL43ACBUNWQQESVM/bundle.json","state":"https://pith.science/pith/Z2MT2PMIJ3OL43ACBUNWQQESVM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2MT2PMIJ3OL43ACBUNWQQESVM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Z2MT2PMIJ3OL43ACBUNWQQESVM","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":"fa74b756c52eddad95f782034d2927c7f99ff6c3530fb6400c7f03df541b74a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-30T17:04:15Z","title_canon_sha256":"fc779abc37eb70cd575e84680901f23a10845c7be228295ea4be937fe405e7e0"},"schema_version":"1.0","source":{"id":"1705.10753","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10753","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10753v2","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10753","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"Z2MT2PMIJ3OL","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z2MT2PMIJ3OL43AC","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z2MT2PMI","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:59da4f9a1588b6622a88987cd9d6ffad88dbe0dcada02bca5d69664a83f91894","target":"graph","created_at":"2026-05-17T23:42:43Z","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":"Originally in 1954 the Tutte polynomial was a bivariate polynomial associated to a graph in order to enumerate the colorings of this graph and of its dual graph at the same time. However the Tutte polynomial reveals more of the internal structure of a graph, and contains even other specializations from other sciences like the Jones polynomial in Knot theory, the partition function of the Pott model in statistical physics, and the reliability polynomial in network theory. In this article, we study the Tutte polynomial associated to more general objects which are the arrangements of hyperplanes.","authors_text":"Hery Randriamaro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-30T17:04:15Z","title":"Tutte Polynomials of Symmetric Hyperplane Arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10753","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:ad5fc8daf9d96aad65ac5eb976b574a32f4f8cc5c4f246aa259356e9ae9ddd7e","target":"record","created_at":"2026-05-17T23:42:43Z","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":"fa74b756c52eddad95f782034d2927c7f99ff6c3530fb6400c7f03df541b74a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-30T17:04:15Z","title_canon_sha256":"fc779abc37eb70cd575e84680901f23a10845c7be228295ea4be937fe405e7e0"},"schema_version":"1.0","source":{"id":"1705.10753","kind":"arxiv","version":2}},"canonical_sha256":"ce993d3d884edcbe6c020d1b684092ab2287290ee3228379f46e013bccc94e39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce993d3d884edcbe6c020d1b684092ab2287290ee3228379f46e013bccc94e39","first_computed_at":"2026-05-17T23:42:43.658632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:43.658632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fil4dYjpoe5phcl8+3ImmF0KpYdlSQsaSAYh30WCEN1S7lQZdgy8cdzSnlJLC/0MaEfLO2eMNCiWRmBKjMYRAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:43.659282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10753","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad5fc8daf9d96aad65ac5eb976b574a32f4f8cc5c4f246aa259356e9ae9ddd7e","sha256:59da4f9a1588b6622a88987cd9d6ffad88dbe0dcada02bca5d69664a83f91894"],"state_sha256":"25d67a8ff521873024392b31c5a8320772be7df86a94c9cd71042c98d0309a22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OCurdLkQzq7th+r81mNsARXMQ52saNr23AnvazJCjDJKbLlzLY5ivs7JsWNfXy4bxqXbYRvAYRYoKkA8NCCKBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:28:29.619911Z","bundle_sha256":"22bf92a23b218b38e8ce7a5c49a7b5f8b9f1425055c40f914c353a4dc2506d35"}}