{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BNWPD7RIBZRT6OGEMVH42SMIL5","short_pith_number":"pith:BNWPD7RI","canonical_record":{"source":{"id":"1105.3220","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-16T21:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"a0124b78162fcc3ac15a04c2877dff837fae49c2a0615ca73e4e56babab65ce1","abstract_canon_sha256":"415597e57c9722781855fe90caa3986324863ba3ef3fee6237d857305d4ce0ef"},"schema_version":"1.0"},"canonical_sha256":"0b6cf1fe280e633f38c4654fcd49885f5c0d672cc4e5e319b771efc5699159d6","source":{"kind":"arxiv","id":"1105.3220","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3220","created_at":"2026-05-18T04:17:02Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3220v3","created_at":"2026-05-18T04:17:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3220","created_at":"2026-05-18T04:17:02Z"},{"alias_kind":"pith_short_12","alias_value":"BNWPD7RIBZRT","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BNWPD7RIBZRT6OGE","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BNWPD7RI","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BNWPD7RIBZRT6OGEMVH42SMIL5","target":"record","payload":{"canonical_record":{"source":{"id":"1105.3220","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-16T21:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"a0124b78162fcc3ac15a04c2877dff837fae49c2a0615ca73e4e56babab65ce1","abstract_canon_sha256":"415597e57c9722781855fe90caa3986324863ba3ef3fee6237d857305d4ce0ef"},"schema_version":"1.0"},"canonical_sha256":"0b6cf1fe280e633f38c4654fcd49885f5c0d672cc4e5e319b771efc5699159d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:02.388246Z","signature_b64":"V0uktUhl/C/kYqHxORfHnjR0EcLeXIdoI4xUqIoR4V5gfXI/pgLDEc/b1TT9dpqZ2bCTURYgyo1XA43rKgoNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b6cf1fe280e633f38c4654fcd49885f5c0d672cc4e5e319b771efc5699159d6","last_reissued_at":"2026-05-18T04:17:02.387622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:02.387622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.3220","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mpOk4oWL3r0+It+K3cdbPXULEsXXvAGhqoQLiSCeUDS6twoav0CsWkm+8fHAu20qDoeTb24658ujn2vvhJ1rAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:52:15.247843Z"},"content_sha256":"34d6799938318853231a2b7b54dcf802f7204891c881a1eec5a392bd074b2dc1","schema_version":"1.0","event_id":"sha256:34d6799938318853231a2b7b54dcf802f7204891c881a1eec5a392bd074b2dc1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BNWPD7RIBZRT6OGEMVH42SMIL5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic matroids, Tutte polynomial, and toric arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luca Moci, Michele D'Adderio","submitted_at":"2011-05-16T21:12:43Z","abstract_excerpt":"We introduce the notion of an arithmetic matroid, whose main example is given by a list of elements of a finitely generated abelian group. In particular we study the representability of its dual, providing an extension of the Gale duality to this setting. Guided by the geometry of generalized toric arrangements, we provide a combinatorial interpretation of the associated arithmetic Tutte polynomial, which can be seen as a generalization of Crapo's formula for the classical Tutte polynomial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3220","kind":"arxiv","version":3},"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":"2026-05-18T04:17:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFFlEOMcB3/J7C8j0F0jyY3KuH7b8bRt+bkILgJEBoLxIm7pUOeTQhSdKol9N/UPbfw1AydKsKy/0vWCGrV0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:52:15.248183Z"},"content_sha256":"a16d5a92f7907dc4e698d02f336ee6e1d3606fcd3bf6601455eb0da782f9f0ab","schema_version":"1.0","event_id":"sha256:a16d5a92f7907dc4e698d02f336ee6e1d3606fcd3bf6601455eb0da782f9f0ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNWPD7RIBZRT6OGEMVH42SMIL5/bundle.json","state_url":"https://pith.science/pith/BNWPD7RIBZRT6OGEMVH42SMIL5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNWPD7RIBZRT6OGEMVH42SMIL5/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":"2026-06-24T21:52:15Z","links":{"resolver":"https://pith.science/pith/BNWPD7RIBZRT6OGEMVH42SMIL5","bundle":"https://pith.science/pith/BNWPD7RIBZRT6OGEMVH42SMIL5/bundle.json","state":"https://pith.science/pith/BNWPD7RIBZRT6OGEMVH42SMIL5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNWPD7RIBZRT6OGEMVH42SMIL5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BNWPD7RIBZRT6OGEMVH42SMIL5","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":"415597e57c9722781855fe90caa3986324863ba3ef3fee6237d857305d4ce0ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-16T21:12:43Z","title_canon_sha256":"a0124b78162fcc3ac15a04c2877dff837fae49c2a0615ca73e4e56babab65ce1"},"schema_version":"1.0","source":{"id":"1105.3220","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3220","created_at":"2026-05-18T04:17:02Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3220v3","created_at":"2026-05-18T04:17:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3220","created_at":"2026-05-18T04:17:02Z"},{"alias_kind":"pith_short_12","alias_value":"BNWPD7RIBZRT","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BNWPD7RIBZRT6OGE","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BNWPD7RI","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:a16d5a92f7907dc4e698d02f336ee6e1d3606fcd3bf6601455eb0da782f9f0ab","target":"graph","created_at":"2026-05-18T04:17:02Z","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 introduce the notion of an arithmetic matroid, whose main example is given by a list of elements of a finitely generated abelian group. In particular we study the representability of its dual, providing an extension of the Gale duality to this setting. Guided by the geometry of generalized toric arrangements, we provide a combinatorial interpretation of the associated arithmetic Tutte polynomial, which can be seen as a generalization of Crapo's formula for the classical Tutte polynomial.","authors_text":"Luca Moci, Michele D'Adderio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-16T21:12:43Z","title":"Arithmetic matroids, Tutte polynomial, and toric arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3220","kind":"arxiv","version":3},"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":"sha256:34d6799938318853231a2b7b54dcf802f7204891c881a1eec5a392bd074b2dc1","target":"record","created_at":"2026-05-18T04:17:02Z","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":"415597e57c9722781855fe90caa3986324863ba3ef3fee6237d857305d4ce0ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-16T21:12:43Z","title_canon_sha256":"a0124b78162fcc3ac15a04c2877dff837fae49c2a0615ca73e4e56babab65ce1"},"schema_version":"1.0","source":{"id":"1105.3220","kind":"arxiv","version":3}},"canonical_sha256":"0b6cf1fe280e633f38c4654fcd49885f5c0d672cc4e5e319b771efc5699159d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b6cf1fe280e633f38c4654fcd49885f5c0d672cc4e5e319b771efc5699159d6","first_computed_at":"2026-05-18T04:17:02.387622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:02.387622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V0uktUhl/C/kYqHxORfHnjR0EcLeXIdoI4xUqIoR4V5gfXI/pgLDEc/b1TT9dpqZ2bCTURYgyo1XA43rKgoNAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:02.388246Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3220","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34d6799938318853231a2b7b54dcf802f7204891c881a1eec5a392bd074b2dc1","sha256:a16d5a92f7907dc4e698d02f336ee6e1d3606fcd3bf6601455eb0da782f9f0ab"],"state_sha256":"bab055e4b49e5a4b141d3219f60b60c9dfd2d6f505c9684e159a1ad398c0a1da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tc76Eh3LoN/FK+uMVaAe2iMXG1Zx2nfr/VGU71HVYAjiT47ENZ1geMEbRLtXBBjdgICVHPrKqaC3dHfMa+QVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:52:15.250235Z","bundle_sha256":"2c61a6d7347c0bc4e78fdf1361115d8d5f0a96f52e77c4a0870d034a6466bfd1"}}